The structural, elastic and thermodynamic properties of the cotunnite-type phase of Hafnia under high pressure from first-principles calculations

The structural, elastic, and thermodynamic properties of the cotunnite-type phase of hafnium dioxide (HfO₂) under high pressure are investigated using pseudopotential plane-wave methods within the PerdewBurkeErnzerhof (PBE) form of generalized gradient approximation (GGA). The obtained results are consistent well with the experimental data and those calculated by others. The elastic properties under high pressure are studied for the first time. We note that the elastic constants, bulk modulus, shear modulus, Youngs modulus, compressional, and shear wave velocities as well as Debye temperature increase monotonically with increasing pressure. By analyzing G/B and Poissons ratio, the brittleductile behavior is assessed. In addition, polycrystalline elastic properties are also obtained successfully for a complete description of elastic properties. Through the quasi-harmonic Debye model, the pressure P and temperature T dependence of the bulk modulus B, variation of the thermal expansion α, heat capacity C_V, and Grüneisen constant γ are studied systematically. At low temperatures, C_V is proportional to T³, and C_V tends to the DulongPetit limit at higher temperatures.